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GRO J2058+42, a transient 198 second x-ray pulsar, was discovered by theBurst and Transient Source Experiment (BATSE) on the Compton Gamma-RayObservatory (CGRO), during a "giant" outburst in 1995 September-October. Thetotal flux peaked at about 300 mCrab (20-50 keV) as measured by Earthoccultation. The pulse period decreased from 198 s to 196 s during the 46-dayoutburst. The pulse shape evolved over the course of the outburst and exhibitedenergy dependent variations. BATSE observed five additional weak outbursts fromGRO J2058+42, each with two week duration and peak pulsed flux of about 15mCrab (20-50 keV), that were spaced by about 110 days. An observation of the1996 November outburst by the Rossi X-ray Timing Explorer (RXTE) ProportionalCounter Array (PCA) localized the source to within a 4\arcmin radius errorcircle (90 % confidence) centered on R.A. = 20h 59m.0, Decl. = 41 deg 43 arcmin(J2000). Additional shorter outbursts with peak pulsed fluxes of about 8 mCrabwere detected by BATSE halfway between the first four 15 mCrab outbursts. TheRXTE All-Sky Monitor detected all 8 weak outbursts with approximately equaldurations and intensities. GRO J2058+42 is most likely a Be/X-ray binary thatappears to outburst at periastron and apastron. No optical counterpart has beenidentified to date and no x-ray source was present in the error circle inarchival ROSAT observations.Comment: 19 pages including 10 figures. Accepted for publication in the  Astrophysical Journa